Nearly 125,000 people have been evacuated via humanitarian corridors from conflict zones in Ukraine, Ukrainian President Volodymyr Zelenskyy said in a video address on Sunday as the Russian invasion continues to be met by fierce resistance.

"Today the key task is Mariupol," he said, adding that a humanitarian supply convoy was now only 80 kilometers (50 miles) away from the besieged port city where more than 400,000 people are trapped.

The Russian military said last week that that it had enforced a new cease-fire in Ukraine and opened humanitarian corridors in five cities.

In the capital Kyiv as well as in the major cities of Chernihiv, Sumy, Kharkiv and the particularly embattled port city of Mariupol, people should be able to get to safety, Ukrainian authorities said Tuesday. Ukraine began evacuating civilians from the northeastern city of Sumy and from the town of Irpin near Kyiv, Ukrainian officials said.

Sumy Governor Dmitro Zhivitskiy said in a video statement that the first buses had already departed Sumy for the city of Poltava, further west. He said priority would be given to the disabled, pregnant women and children in orphanages. A short video clip released by presidential adviser Kyrolo Tymoshenko showed a red bus with some civilians on board.

"It has been agreed that the first convoy will start at 10 a.m. (8:00 a.m. GMT) from the city of Sumy. The convoy will be followed by the local population in personal vehicles," Deputy Prime Minister Iryna Vereshchuk said in a televised statement.

Russian agencies also reported last week that Moscow will open daily humanitarian corridors to evacuate civilians fleeing fighting in Ukraine to its territory, despite Kyiv insisting that no evacuation routes should lead to Russia.

"Humanitarian corridors towards the Russian Federation will now be opened, without any agreements, every day from 10:00 a.m.," Russian Defense Ministry official Mikhail Mizintsev was quoted as saying by Russian agencies. He said evacuation routes in other directions would proceed "in agreement with the Ukrainian side."

"We ask the International Committee of the Red Cross and the United Nations to work closely with Ukrainian authorities on the ground to inform the population about this Russian initiative," he said.

He also said the Russian army was working "closely with Ukrainian representatives" to open another three humanitarian corridors.